1. Field of the Invention
The present invention relates to a non-transitory computer-readable storage medium storing a program for deciding an exposure condition in an exposure apparatus, a decision method, and a computer.
2. Description of the Related Art
In an exposure step using an exposure apparatus, it is generally required to transfer, based on desired image characteristics, a photoresist (resist) applied to the surface of a substrate such as a wafer and hardly change the image characteristics in case of variations (errors) in the focal point, exposure amount, and the like. Techniques of optimizing (deciding) an exposure condition in an exposure apparatus have been proposed in Japanese Patent Laid-Open No. 2008-166777, T. Matsuyama, et. al., “A Study of Source & Mask Optimization for ArF Scanners”, Proc. of SPIE, USA, SPIE, 2009, Vol. 7274, p. 727408 (literature 1), and Linyong Pang, et. al., “Optimization from Design Rules, Source and Mask, to Full Chip with a Single Computational Lithography Framework: Level-Set-Methods-based Inverse Lithography Technology (ILT)”, Proc. of SPIE, USA, SPIE, 2010, Vol. 7640, 764000 (literature 2). The image characteristics include, for example, the size and shape of an image, the contrast, the margin of the image size for the exposure amount, and the margin of the image size for the focal point. The exposure conditions include the shape of an effective light source (the light intensity distribution formed on the pupil plane of the illumination optical system), the numerical aperture (NA) and aberration of the projection optical system, the pattern (size and shape) of a mask arranged on the object plane of the projection optical system, and the transmittance of the mask.
When optimizing an exposure condition, a condition that maximizes the target of interest of the user, for example, the depth of focus (DOF) for the line width of a specific image is searched for concerning the effective light source or the mask pattern. Note that the exposure condition optimization is not limited to searching for the exposure condition that increases the DOF. For example, if the aberration of the projection optical system of the exposure apparatus always varies, searching for an exposure condition that suppresses the influence of such aberration variation is desired. For an exposure apparatus in which the fluctuation of the exposure amount is small, searching for an exposure condition to obtain not the margin of the exposure amount but the depth of focus (margin for the focal point) is desired. If the stage of an exposure apparatus largely vibrates, searching for an exposure condition with which the image characteristics hardly change for the stage vibration is desired. That is, there exist wider needs for exposure condition optimization, and various kinds of exposure conditions are optimized.
In the exposure condition optimization, generally, an evaluation item (for example, DOF, NILS, or line width) is set in advance, and an exposure condition is optimized such that the value of the evaluation item (evaluation amount) satisfies the standard. For an evaluation item such as the DOF or NILS (Normalized Image Log Slope) whose evaluation amount is preferably as large as possible, optimizing the exposure condition means maximizing the evaluation amount. On the other hand, for an evaluation item such as a line width error whose evaluation amount is preferably as small as possible, optimizing the exposure condition means minimizing the evaluation amount. More specifically, the exposure condition optimization is executed by obtaining an evaluation amount under a given exposure condition (parameters that define the shape of the effective light source or the shape of the mask pattern) and changing the exposure condition in accordance with the evaluation amount (repetitively changing the exposure condition). The exposure condition changing method depends on a mathematical method or algorithm, and various methods have been proposed. An evaluation item (evaluation amount) of interest will be referred to as an optimization cost hereinafter. Note that the optimization cost is sometimes called a merit function or a metric, or simply as a cost or a merit.
In the related art, an evaluation item of interest is directly set as an optimization cost. For example, in Japanese Patent Laid-Open No. 2008-166777, the line width (CD) uniformity or the like is set as the optimization cost, and the optimum effective light source shape is obtained. In literature 1, a common process window or OPE characteristic (line width) is set as the optimization cost, and the optimum effective light source shape or mask pattern is obtained. In literature 2, an edge placement error is set as the optimization cost, and the exposure condition is optimized.
However, the present inventor has found that in the related art, the exposure condition cannot be optimized in some cases because the evaluation item of interest is directly set as the optimization cost.
In the related art, as described above, the optimization cost value is obtained while changing an exposure condition, and the direction in which the exposure condition is changed is decided based on the change in the optimization cost value, thereby making the exposure condition gradually converge to an optimum condition. Hence, it is important that the optimization cost value changes every time the exposure condition changes.
For example, examine optimization of the exposure condition to maximize the DOF. In the related art, the DOF is directly set as the optimization cost, and the exposure condition is changed to maximize the optimization cost. Assume that the value of the DOF becomes large when the exposure condition is changed. This suggests that the value of the DOF can be made larger at a high probability by changing the exposure condition in the direction in which it has been changed. Alternatively, assume that the value of the DOF becomes small when the exposure condition is changed. This suggests that the value of the DOF can be made larger at a high probability by changing the exposure condition in a direction reverse to the direction in which it has been changed.
If the value of the DOF does not change even when the exposure condition is changed, the direction in which the exposure condition should be changed cannot be known. More specifically, even when the effective light source shape or the mask pattern is changed, the value of the DOF is hardly obtained (that is, the DOF continuously takes a value of 0) in some cases. When the optimization cost continuously takes a specific value, the direction in which the exposure condition is to be changed cannot be known. Hence, the exposure condition cannot be optimized.
To avoid this problem, the range of exposure condition change (search) may be narrowed. In this case, however, the exposure condition can be searched for in a very narrow range and optimized in the limited narrow range. This is not practical because the exposure condition cannot globally be optimized. As described above, the exposure condition cannot be optimized sometimes. However, the related art has mentioned neither the problem nor the solution to it, as a matter of course.